| 一类具幂零奇点的五次系统中心条件及极限环分支 |
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| 引用本文： | 李锋,金银来.一类具幂零奇点的五次系统中心条件及极限环分支[J].数学研究及应用,2011,31(5):937-945. |
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| 作者姓名： | 李锋 金银来 |
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| 作者单位： | 临沂大学理学院, 山东 临沂 276005;临沂大学理学院, 山东 临沂 276005 |
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| 基金项目： | 山东省自然科学基金(Grant No.Y2007A17) |
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| 摘 要： | In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.
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| 关 键 词： | three-order nilpotent critical point center-focus problem bifurcation of limit cycles quasi-Lyapunov constant. |
| 收稿时间： | 5/9/2010 12:00:00 AM |
| 修稿时间： | 2010/11/20 0:00:00 |
Center Conditions and Bifurcation of Limit Cycles at Nilpotent Critical Point in a Quintic Lyapunov System |
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| Feng LI and Yin Lai JIN.Center Conditions and Bifurcation of Limit Cycles at Nilpotent Critical Point in a Quintic Lyapunov System[J].Journal of Mathematical Research with Applications,2011,31(5):937-945. |
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| Authors: | Feng LI and Yin Lai JIN |
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| Institution: | School of Science, Linyi University, Shandong 276005, P. R. China |
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| Abstract: | In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. |
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| Keywords: | three-order nilpotent critical point center-focus problem bifurcation of limit cycles quasi-Lyapunov constant |
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